Time-Complexity Semantics for Feasible Affine Recursions

The authors’ ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable (ATR types are confined to levels 0, 1, and 2). A limitatio...

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Bibliographic Details
Published inComputation and Logic in the Real World Vol. 4497; pp. 205 - 217
Main Authors Danner, Norman, Royer, James S.
Format Book Chapter
LanguageEnglish
Published Germany Springer Berlin / Heidelberg 2007
Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Base Type
Elimination Rule
Recursive Call
Type Context
Typing Rule
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Summary:The authors’ ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable (ATR types are confined to levels 0, 1, and 2). A limitation of the original version of ATR is that the only directly expressible recursions are tail-recursions. Here we extend ATR so that a broad range of affine recursions are directly expressible. In particular, the revised ATR can fairly naturally express the classic insertion- and selection-sort algorithms, thus overcoming a sticking point of most prior implicit-complexity-based formalisms. The paper’s main work is in extending and simplifying the original time-complexity semantics for ATR to develop a set of tools for extracting and solving the higher-type recurrences arising from feasible affine recursions.
ISBN:9783540730002
3540730001
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-540-73001-9_22